Second 7 Wonders, Race for the Galaxy, Betrayal at House on the Hill, Cthulhu Wars, Seasons and Pandemic.
Although I'd actually recommend Forbidden Island or Forbidden Desert over Pandemic - the play structure is similar, although the mechanics are different, and I think the art and flavor are phenomenal. (In Forbidden Island, you're playing as a team of archeologists trying to locate lost artifacts before the island sinks out from underneath you, while in Forbidden Desert you're trying to repair an ancient flying machine before you die of thirst in the desert, or get buried in sand.)
Some of my other favorites:
Dungeon Lords: Worker placement game for 4 players. You're playing as an evil dungeon lord, trying to protect your lair from those pesky heroic adventurers trying to kill you. You recruit monsters (slimes, goblins, vampires, dragons), build traps, and develop your dungeon during the worker placement section, and then there's a puzzle section where you try and deal with the adventurers you've attracted with a minimum of pain. The worker placement is pretty interesting too - each action has several different modes, and which one you get is determined by the order workers are placed on the action - which you don't know until after you've selected your actions. So a big part of strategy is predicting what actions the other players will take so that you can land on the modes you want. And the flavor is pretty fun. One example is food: the first mode for food is to pay 1 gold for 2 food (your minion goes to the village and pays for food). The second mode is to go up in evil reputation for 3 food (the villagers refuse to sell you food, so you threaten to burn down the village, and they give you food). The third mode is to go up in evil reputation twice, and get 3 food and a gold (the villagers refuse to give you food, even when threatened, so you burn down the village and find food plus the gold that the first minion payed them). Another example is the "Magic room". Two imps and a romantic dinner go in, three imps come out! It's magic!
Tales of Arabian Nights: Admittedly, this is less of a board game, and more of a choose your own adventure story with multiple people running around. There's almost no strategy involved, you just run around making questionable decisions (I recommend courting everything that moves) and getting bewitched, crippled, and turned into monkeys.
Shadows over Camelot & Battlestar Galactica: not entirely the same, but both are mostly coopertive games where everyone's working together, but 1 or more people is secretly a traitor. Both are fun and flavorful, and I recommend both. (and actually, they are about as similar to each other as Pandemic is to Forbidden Island or Forbidden Desert.)
Atlantis: I like to describe it as "Candy Land, only fun". The movement mechanic is similar to Candy Land, but you have multiple meeples to move, and multiple cards to play, and the tiles in the path disappear from behind you as you move (because you're escaping a sinking Atlantis), so it becomes much more strategic than Candy Land could ever be.
Ninja Burger: If you like Munchkin, you'll probably like Ninja Burger. It's another Steve Jackson game, where you're playing as a family of ninjas running a burger joint, and you go on missions to deliver burgers to places like the International Space Station, supervillain lairs, and Camelot. There's less backstabbing than in Munchkin but it's still present, and a lot things that can't be done in other games, (like winning ties or playing cards after dice have been roled) are allowed because you're ninjas.
Hey! That's my Fish!: A 2-4 person 15 minute tile game where you play as penguins sliding around and collecting fish.
Guilds of Cadwallon: 2-8 players (if you have the expansion), about 30-45 min. You're recruiting guilds to join you. I'm not entirely sure how to describe the mechanic better than that, but it's very simple and easy to pick up. The art is beautiful (if a little busy), and it can get very complex very quickly, especially if you're using a large board.
